Download PDF by Dixon M., Kurdachenko L., Subbotin I.: Algebra and number theory. An integrated approach

By Dixon M., Kurdachenko L., Subbotin I.

ISBN-10: 0470496363

ISBN-13: 9780470496367

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EXAMPLE 12— 6(−2)(−3)(−4) ᎏᎏ (−12)(−4)(+1) 5 minus signs; answer is minus. ANSWER −3 Integers Plus More 29 EXAMPLE 13— (−3a4b5c6)(−10a5b100c1000)(5a2b3c) Determine sign first: 2 minus signs, +. Rest of the coefficient: (3)(5)(10) = 150; a4 + 5 + 2 = a11; b5 + 100 + 3 = b108; c6 + 1000 + 1 = c1007. Remember: when you multiply, add the exponents, if the bases are the same. ANSWER +150a11b108c1007 NOTE Notice, big numbers do not make problems hard. (am)n = amn EXAMPLE 14— We’ll do more of this later.

7 means two numbers, +7 and −7. The positive integers is another name for the natural numbers. x positive: x > 0, x is greater than zero. The nonnegative integers is another name for the whole numbers. x negative: x < 0, x is less than zero. Even integers: 0, Ϯ2, Ϯ4, Ϯ6, Ϯ8 . . Odd integers: Ϯ1, Ϯ3, Ϯ5, Ϯ7, . . and so on. 3 means +3. EXAMPLE 1— Graph the set −4, −1, 0, 3. –5 –4 –3 –2 –1 0 1 2 3 4 23 Copyright © 2006, 1999 by The McGraw-Hill Companies, Inc. Click here for terms of use. 24 BOB MILLER’S ALGEBRA FOR THE CLUELESS EXAMPLE 2— Graph all even integers between −6 and 7.

2x + 3x = 45. Solving, we get x = 9. One piece is 2x = 2(9) = 18. The other piece is 3x = 3(9) = 27. NOTES 1. Ratios have two common notations: 2:3 (read: “two to three”) or 2/3. 2. E X A M P L E 5 — 49 50 BOB MILLER’S ALGEBRA FOR THE CLUELESS E X A M P L E 5 — In In a triangle, the ratio of the angles is 3:4:5. Find the angles. As in Example 4, the angles will be 3x, 4x, and 5x. 3x + 4x + 5x = 180, since the angles of a triangle add up to 180°. Solving, x = 15, and the angles are 45°, 60°, and 75°.

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Algebra and number theory. An integrated approach by Dixon M., Kurdachenko L., Subbotin I.


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